1. Review of Mesoscopic Thermal Transport Measurements
Li Shi
IBM Research
&
University of Texas at Austin
IMECE01, New York, November 12, 2001

2. Outline 1. Thermal Transport in Micro-Nano Devices
2. Thermal Property Measurements of Low-Dimensional
Structures:
-- 2D: Thin Films
-- 1D: Nanotubes, Nanowires
-- Quantized Thermal Conductance
3. Thermal Microscopy of Micro-Nano Devices

3. 1. Micro-Nano Devices Gate Drain Source Nanowire Channel
MEMS/NEMS
Bio Chip (Wu et al., Berkeley)
Microelectronics
Si FET (Hu et al., Berkeley)
Gate
Drain
Source
Nanowire Channel
Consisting of 2D and/or 1D structures

4. Molecular Electronics
Nanotube
Nanowire Arrays
(Lieber et al., Harvard)
TubeFET (McEuen et al.,
Berkeley)
Nanotube Logic (Avouris et al., IBM Research)

5. Length Scale - + 1 mm Size of a Microprocessor MEMS Devices 1 mm
Thin Film Thickness in ICs
100 nm
l (Mean free
path at RT)
10 nm
Nanotube/ Nanowire Diameter
1 nm
lF (Fermi
wavelength)
Atom L
W  l: boundary scattering
W  lF: quantized effects
L  l: ballistic transport - + W
1 Å

6. 2. Thermal Conductivity: k = ke + kp
C ~ T d
lst
lst ~ lum 1 3 kp = C v l
Phonon mfp
Specific heat
Sound velocity
lum ~ eQ/ T
If T > Q, C ~ constant
If T << Q, C ~ T d (d: dimension)
Specific heat :
Mean free path:
Static scattering (phonon -- defect, boundary):
lst ~ constant
Umklapp phonon scattering:
lum ~ eQ/ T

7. 2.1 Measurements of Thin-Film Thermal Conductivity
The 3w method -- Cahill, Rev. Sci. Instrum. 61, 802 (1990)
Metal line
Thin Film
I ~ 1w
T ~ I2 ~ 2w
R ~ T ~ 2w
V~ IR ~3w L 2b V
I0 sin(wt)
Si Substrate

8. SOI Thin Films
Ashegi, Leung, Wong, Goodson, Appl. Phys. Lett. 71, 1798 (1997)
2. Ju and Goodson, Appl. Phys. Lett. 74, 3005 (1999)
Courtesy of Ref. 2

9. Anisotropic Polymer Thin Films
Ju, Kurabayashi, Goodson, Thin Solid Films 339, 160 (1999)
By comparing temperature rise of the metal line for different line
width, the anisotropic thermal conductivity can be deduced

10. Superlattices
1. Song, Liu, Zeng, Borca-Tasiuc, Chen, Caylor, Sands, Appl. Phys. Lett. 77, 3154 (2000)
2. Huxtable, Majumdar et al., Micro Therm. Eng. (2001)

11. 2.2 1D Nanostructure: (i) Nanowires
Si Nanowires for Electronic Applications
Bi Nanowires for TE Cooling (Dresselhaus et al., MIT)
Top View
Al2O3 template
Boundary scattering + modified phonon dispersion (group velocity):
 Suppressed thermal conductivity
Volz and Chen, Appl. Phys. Lett. 75, 2065 (1999)

12. (ii) Carbon Nanotube Single Wall Multiwall Super high current
109 A/cm2
Single Wall
-- Semiconducting or Metallic E k
Metal l ic
Semiconducting F
microns
1-2 nm
Multiwall
-- Metallic
10 nm

13. Thermal Conductivity of Nanotubes
Carbon Nanotube:
high v, long l  high k
3000 ~ 6000 W/m-K at room temperature
(e.g. Berber et al., 2000)
Theoretical Expectation:
Previous Measurement of Nanotube Mats:
~ 200 W/m-K
(Hone et al., 2000)
Nanotube mat
Unknown filling factor
Thermal resistance at
tube- tube junctions

14. The 3w method for 1D Structures
-- Lu, Yi, Zhang, Rev. Sci. Instrum. 72, 2996 (2001)
Low frequency: V(3w) ~ 1/k
High frequency: V(3w) ~ 1/C
Tested for a 20 mm dia. Pt wire
Results for a bundle of MW nanotubes:
C ~ linear T dependence, low k ~ 100 W/mK V
I0 sin(wt)
Electrode
Wire
Substrate
3w Mechanism: DT~ V2/k and R ~ Ro + aDT
Applicable to an individual SW nanotube?
-- R4p = Rjunction + Rbulk
-- Rjunction  Rjunction,0 + aDT
-- Rbulk ~ Rbulk (V) even when DT = 0

15. Another 1D Method -- A Hybrid Nanotube Microdevice
Pt heater line
Multiwall nanotube
SiNx beam
Pt heater line
Suspended island

16. Device Fabrication (c) Lithography Photoresist (a) CVD SiNx SiO2
(d) RIE etch
(b) Pt lift-off Pt
(e) HF etch

17. Measurement Scheme Gt = kA/L Thermal Conductance: IQ I R h = h R t R h s
VTE
Thermopower:
Q = VTE/(Th-Ts) T u be Q = IR l l
Environment I T
10 nm multiwall tube
Island
Beam
Pt heater line

18. Measurements Resistance of the Pt line Cryostat: T : 4-350 K
P ~ 10-6 torr
Resistance of the Pt line
Resistance vs. Joule Heat m

19. Thermal Conductivity  T2 l ~ 0.5 mm 14 nm multiwall tube
Room temperature thermal conductivity ~ 3000 W/m-K
k ~ T2 : Quasi 2D graphene behavior at low temperatures
Umklapp scattering ~ 320 K , l ~ 500 nm
Nearly ballistic phonon transport
Kim, Shi, Majumdar, McEuen, Phy. Rev. Lett, in press

20. Thermal Conductivity Interlayer phonon mode filled – 2D
k(T) (W/m K)
T (K)
3000
2000
1000
300
200
100
Interlayer phonon
mode filled – 2D
14 nm individual
MW tube
2.0
80 nm
bundle
Junctions in bundles
reduce k and lst
2.5
Interlayer phonon
mode unfilled – 3D
200 nm bundle

21. Thermopower
For metals w/ hole-type majority carriers:
 T

22. More on 1D Measurements Single Wall Nanotube
Short lst and suppressed k found for Si nanowires (D. Li et al.)
Bi and Bi2Te3 wires to be measured
Challenges of measuring single wall nanotube
Single Wall Nanotube

23. 2.3 Quantized Thermal Conductance
Electron thermal conductance quantization (Molenkamp et al., 1991)
Quantum point contact
Phonon thermal conductance quantization (Schwab et al., 1999)
Quantum of
Thermal Conductance

24. 3. Thermal Microscopy of Micro-Nano Devices
Techniques Spatial Resolution
Infrared Thermometry mm*
Laser Surface Reflectance [1] mm*
Raman Spectroscopy mm*
Liquid Crystals mm*
Near-Field Optical Thermometry [2] < 1 mm Scanning Thermal Microscopy (SThM) < 100 nm
*Diffraction limit for far-field optics
1. Ju & Goodson, J. Heat Transfer 120, 306 (1998)
2. Goodson & Asheghi, Microscale Thermophysical Eng. 11,
225 (1997)

25. Scanning Thermal Microscope
Atomic Force Microscope (AFM) + Thermal Probe
Laser
Deflection
Sensing
Cantilever
Temperature
Sensor
Thermal X T
Sample
Topographic X Z
X-Y-Z
Actuator

26. Thermal Probe
Rts Rt Ts Ta Tt Rc Q

27. Probe Fabrication
200 nm Pt
SiO2
1 mm
SiO2 tip

28. Microfabricated Probes
Pt Line
Tip
Laser Reflector
Pt-Cr
Junction
SiNx Cantilever
Cr line
10 mm
Shi, Kwon, Miner, Majumdar, J. MicroElectroMechanical Sys., 10, p. 370 (2001)

29. Locating Defective VLSI Via
Topography
Tip Temperature Rise (K) 19 21
40 mA
Via
Metal 1 23 28 25
Metal 2
20 mm
Cross Section
Passivation
Metal 2
Collaboration: TI
Shi et al., Int. Reli. Phys.
Sym., p. 394 (2000)
Dielectric
0.4 mm
Via
Metal 1

30. Calibration
S = R
W(mm) S(K/K)
0.56 W

31. Tip-Sample Heat Transfer
Why saturated? W
W , air 
W = 0.2 mm, Air ~ Solid + Liquid
W < 0.1 mm, Air << Solid + Liquid

32. Why GSol Saturated?
Elastic-Plastic Contact of an Asperity and a Plane
What is the thermal conductance at the nano contact?

33. Thermal Transport at Nano Contacts
Modeling results:
GLiq ~ 7 nW/K, GSol ~ 0.8 W/m2-K-Pa
L < Mean free path of air or phonon
Shi and Majumdar, J. Heat Transfer, in press

34. Thermal Imaging of Nanotubes
Multiwall Carbon Nanotube
Distance (nm)
Height (nm)
30 nm 10 5
400
200
-200
-400
Thermal
Topography
Topography
3 V 88 m A 1 1 m m m m
Spatial Resolution V) 30 20 10
400
200
-200
-400 m
30 nm
50 nm
50 nm
Thermal signal (
Distance (nm)
Shi, Plyosunov, Bachtold, McEuen, Majumdar, Appl. Phys. Lett., 77, p (2000)

35. Electron Transport in Nanotube
Ballistic (long mfp)
Diffusive (short mfp) - - + + - -
mfp: electron mean free path
Multiwall
Ballistic (Frank et al., 1998)
Diffusive (Bachtold et al., 2000)
Single Wall Semiconducting
Diffusive (McEuen et al., 2000)
Single Wall Metallic
Ballistic at low bias (Bachtold ,et al.)
Diffusive at high bias (Yao et al., 2000)

36. Dissipation in Nanotube
bulk
Electrode
Electrode
Junction
Diffusive – Bulk Dissipation T
T profile 
diffusive or ballistic X
Ballistic – Junction Dissipation T X

37. Multiwall Nanotube Thermal Topographic DTtip A B 3 K 1 mm
Diffusive at low and high biases B A A B

38. Metallic Single Wall Nanotube
Low bias: ballistic
contact dissipation
High bias: diffusive
bulk dissipation
Optical phonon
Topographic
Thermal
DTtip A B C D
2 K
1 mm

39. Semiconducting Single Wall Nanotube
Topographic
Thermal
Bulk heating at low and
high biases  diffusive A B
DTtip
2 K
1 mm
Nanotube field-effect transistor
Contact
Nanotube Vs
Vd = gnd
SiO2
Si Gate Vg

40. More on Thermal Microscopy
UHV and low-temperature thermal and thermoelectric microscopy
Near-field radiation and solid conduction through a point contact, e.g. in thermally-assisted magnetic writing and thermomechanical data storage

41. Summary Nanotube Thermal Conductivity --Majumdar, McEuen
Thin film Thermal Conductivity
--Cahill, Goodson, Chen, Majumdar L 2b V
I0 sin(wt)
Thermal Conductance Quantum
--Roukes
Thermal Microscopy of Nanotubes
-- Majumdar